Pinball flasher dome
Note:
  
  This answer is connected to this one so I'll not go into details
  as much.


Final result:



Steps:


Create Sphere and remove bottom half of it.
Add Solidify Modifier and set desired thickness. Apply this modifier.





Select outer side of the object (you can select top vertex and hit Ctrl+NumPad+ couple of times), then hide it H.





From the inner part of the mesh select needed edges and scale them down.





You can make bottom edge even by scaling it 0 on the Z axis.
Alt+H to unhide outer part of the mesh.
Select all and Recalculate Normals.
In Object Mode choose Smooth Shading and Auto Smooth in Data tab.